According to the revised New American Bible, the Annunciation, when the angel Gabriel tells Mary she has been chosen to be the mother of God, the Son, is the exact moment of the Incarnation.
The encounter, with Mary’s questioning and acceptance, is described in Luke 1: 26-38. This liturgical feast, first celebrated in the East, was introduced in Rome between 660 and 680. The oldest liturgical books called it “Adnuntiatio Domini,” the Annunciation of the Lord, but during the Middle Ages it was popularly celebrated as a Marian feast, the Annunciation to the Virgin Mary. The 1969 revision of the Roman liturgical calendar restored the feast as a solemnity of the Lord and restored its ancient title.